Problem 226

A Scoop of Blancmange

The *blancmange curve* is the set of points (`x`,`y`) such that 0 `x` 1 and ,

where `s`(`x`) = the distance from `x` to the nearest integer.

The area under the blancmange curve is equal to ½, shown in pink in the diagram below.

Let `C` be the circle with centre (¼,½) and radius ¼, shown in black in the diagram.

What area under the blancmange curve is enclosed by `C`?

Give your answer rounded to eight decimal places in the form *0.abcdefgh*

**
These problems are part of
Project Euler
and are licensed under
CC BY-NC-SA 2.0 UK
**